The Rastrigin Function is a fairly complicated mathematical function often used as a test problem for numerical optimization algorithms. There are actually several variations of the function. A common version is:

f(x,y) = 20 + (x^2 – 10*cos(2*pi*x)) + (y^2 – 10*cos(2*pi*y))

where x and y can be between -5.12 and +5.12.

The Rastrigin function has an interesting shape when plotted in 3D. See the image below. The function has a minimum value of 0.0 when x = 0.0 and y = 0.0.

A very common way to plot math functions is by using the MatLab program but I wanted to use SciLab, a close-but-not-exact clone of the MatLab program (which can be a bit pricey). Here are SciLab commands that generated the nice visualization of the Rastrigin function:

x1 = linspace(-5.12,5.12,100);
x2 = linspace(-5.12,5.12,100);
[XX1,XX2]=meshgrid(x1,x2);
Z = (XX1.^2 – 10*cos(2*%pi*XX1)) + (XX2.^2 – 10*cos(2*%pi*XX2)) + 20; f=scf();
f.color_map = jetcolormap(64);
plot3d1(x1,x2,Z’);